Use of the mantle magnitudeM m for the reassessment of the moment of historical earthquakes

The mantle magnitudeM _m is used on a dataset of more than 180 wavetrains from 44 large shallow historical earthquakes to reassess their moments, which in many cases had been previously estimated only on the basis of the earthquake's rupture area. We provide 27 new or revised values ofM _o, based on the spectral amplitudes of surface waves recorded at a number of stations, principally Uppsala and Pasadena. Among them, and most significantly, we document a large low-frequency component to the source of the 1923 Kanto earthquake: the low-frequency seismic moment is 2.9×10²⁸ dyn-cm, in accord with geodetic observations. On the other hand, we revise downwards the seismic moment of the 1906 Ecuador event, which did not exceed 6×10²⁸ dyn-cm.Finally, the study of the 1960 Chilean and 1964 Alaskan earthquakes whose exceptionally large moments are properly retrieved throughM _m measurements, serves proof that this approach performs flawlessly even for the very greatest earthquakes, and is therefore successful in its goal to avoid the saturation effects plaguing any magnitude scale measured at a fixed period.     

Automatic detection,location and quantification of earthquakes: Application to tsunami warning

We describe a fully automated seismic event detection and location system, providing for real-time estimates of the epicentral parameters of both local and distant earthquakes. The system uses 12 telemetered short-period stations, with a regional aperture of 350 km, as well as two 3-component broad-band stations. Detection and location of teleseismic events is achieved independently and concurrently on the short-period and long-period channels. The long-period data is then used to obtain an estimate of the seismic momentM ₀ of the earthquake through the mantle magnitudeM _m, as introduced byOkal andTalandier (1989). In turn, this estimate ofM ₀ is used to infer the expected tsunami amplitude at Papeete, within 15 minutes of the recording of Rayleigh waves. The performance of the method is discussed in terms of the accuracy of the epicentral parameters and seismic moment obtained in real time, as compared to the values later published by the reporting agencies. Our estimates are usually within 3 degrees of the reported epicenter, and the standard deviation on the seismic moment only 0.19 unit of magnitude for a population of 154 teleseismic events.     

One-station estimates of seismic moments from the mantle magnitudeM m: The case of the regional field (1.5°≤Δ≤15°)

We extend to the regional field of distances the procedure of one-station estimation of seismic moments using the mantle magnitudeM _m, as introduced earlier in the case of teleseismic events. A theoretical analysis of the validity of the asymptotic expansion of normal modes in terms of surface waves, which was used in the development ofM _m, upholds the validity of the algorithm for distances as short as 1.5°. This is confirmed by the analysis of a dataset of 149 GEOSCOPE records obtained at distances ranging from 1.5 to 15°, from earthquakes with moments between 10²⁴ and 2.5×10²⁷ dyn-cm. The performance ofM _m as measured in terms of average residual with respect to published values ofM ₀, and standard deviation of the residuals, is not degraded in this distance range, with respect to the teleseismic case. This indicates that the mantle magnitudeM _mcan be reliably used at regional distances, notably for tsunami warning applications.     

Spectral magnitude and seismic radiated energy computed from CDSN records

We have employed 10 digital records and computed the spectral magnitude and the seismic radiated energy for 18 large earthquakes (M _s≥6) occurred in Eur-asian belt during 1986–1989. The nine digital stations (CD-SN) distribute all over China and one in Germany. The spectral magnitudes of various period have different stability among stations. The stability is better for maximum spectral magnitudemi and seismic radiated energyE, their differences among stations are smaller, especially for the stations where the ray path main penetrates the low mantle. But the stability of corner period is usually not good. The relation between seismic radiated energy and seismic moment magnitudeM _w is lg (E)=1.5Mw+c, wherec is a constant. The maximum spectral magnitudemi=M _w+0.1, it is consistant with theoretical prediction. The Chinese version of this paper appeared in the Chinese edition ofActa Seismologica Sinica,15, 418–426, 1993. This work supported by the Deutsche Forschungsgemeinschaft, Bonn, F. R. Germany. The support is grateful acknowledge.     

M m: A variable-period mantle magnitude for intermediate and deep earthquakes

We extend to the case of intermediate and deep earthquakes the mantle magnitude developed for shallow shocks byokal andTalandier (1989). Specifically, from the measurement of the spectral amplitude of Rayleigh waves at a single station, we obtain a mantle magnitude,M _m, theoretically related to the seismic moment of the event through $$M_m = \log _{10} M_0 - 20.$$ The computation ofM _minvolves two corrections. The distance correction is the same as for shallow shocks. For the purpose of computing the frequency-dependent source correction, we define three depth windows: Intermediate (A) (75 to 200 km); Intermediate (B) (200–400 km) and Deep (over 400 km). In each window, the source correctionC _S is modeled by a cubic spline of log₁₀ T. Analysis of a dataset of 200 measurements (mostly from GEOSCOPE stations) shows that the seismic moment of the earthquakes is recovered with a standard deviation of 0.23 units of magnitude, and a mean bias of only 0.14 unit. These figures are basically similar to those for shallow events. Our method successfully recognizes truly large deep events, such as the 1970 Colombia shock, and errors due to the potential misclassification of events into the wrong depth window are minimal.     

Quantification relations between the sourc eparameters

The various useful source-parameter relations between seismic moment and common use magnitude lg(M ₀) andM _s,M _L,m _b; between magnitudesMs andM _L,M _s andm _b,M _L andm _b; and between magnitudeM _s and lg(L) (fault length), lg (W) (fault width), lg(S) (fault area), lg(D) (average dislocation);M _L and lg(f _c) (corner frequency) have been derived from the scaling law which is based on an “average” two-dimensional faulting model of a rectangular fault. A set of source-parameters can be estimated from only one magnitude by using these relations. The average rupture velocity of the faultV _r=2.65 km/s, the total time of ruptureT(s)=0.35L (km) and the average dislocation slip rateD=11.4 m/s are also obtained. There are four strong points to measure earthquake size with the seismic moment magnitudeM _w.

1. The seismic moment magnitude shows the strain and rupture size. It is the best scale for the measurement of earthquake size.
2. It is a quantity of absolute mechanics, and has clear physical meaning. Any size of earthquake can be measured. There is no saturation. It can be used to quantify both shallow and deep earthquakes on the basis of the waves radiated.
3. It can link up the previous magnitude scales.
4. It is a uniform scale of measurement of earthquake size. It is suitable for statistics covering a broad range of magnitudes. So the seismic moment magnitude is a promising magnitude and worth popularization.

     

内蒙古中西部地区中小地震矩震级研究

基于S震相"S窗"内的波形信号识别、品质因子Q(f)和22个台站场地响应,利用2009~2016年3月内蒙古中西部地区地震的波形资料,反演了182次中小地震的震源波谱参数,得到这些小震的零频幅值及其拐角频率,据此计算了这些地震的地震矩M_0、矩震级M_W和应力降Δσ。利用回归分析方法得到了近震震级与矩震级、矩震级与应力降的关系式。分析表明,近震震级与矩震级、矩震级与应力降呈线性关系。可见,将矩震级纳入地震的快报与正式目录中,可以丰富地震观测报告内容,更好地为地震应急和地震科研服务。     

Analysis and automatic processing in near-field of eight 1992–1994 tsunamigenic earthquakes: Improvements towards real-time tsunami warning

We study eight tsunamigenic earthquakes of 1992–1994 with data from single near-field 3-component long-period stations. The analysis is made from the standpoint of tsunami warning by an automatic process which estimates the epicentral location and the seismic moment through the variable-period mantle magnitudeM _m . Simulations of early warning based on the real-time computation of the seismic moment are also tested with this system, which would give a justified warning in each region of tsunami potentiality. By exploiting the dependence of moment rate release with frequency, the system has the capability of recognizing both tsunami earthquakes such as the 1992 Nicaragua and 1994 Java events, as well as instances of the opposite case of low-frequency deficiency, interpreted as indicating a deeper than normal source (1993 Guam event). We report both the results of delayed-time processing of the near-field stations, and the actual real-time warnings at PPT, which confirm the former.     

Magnitude scale for the Central American tsunamis

Based on the tsunami data in the Central American region, the regional characteristic of tsunami magnitude scales is discussed in relation to earthquake magnitudes during the period from 1900 to 1993. Tsunami magnitudes on the Imamura-Iida scale of the 1985 Mexico and 1992 Nicaragua tsunamis are determined to bem=2.5, judging from the tsunami height-distance diagram. The magnitude values of the Central American tsunamis are relatively small compared to earthquakes with similar size in other regions. However, there are a few large tsunamis generated by low-frequency earthquakes such as the 1992 Nicaragua earthquake. Inundation heights of these unusual tsunamis are about 10 times higher than those of normal tsunamis for the same earthquake magnitude (M _s =6.9–7.2). The Central American tsunamis having magnitudem>1 have been observed by the Japanese tide stations, but the effect of directivity toward Japan is very small compared to that of the South American tsunamis.     

Determination of source duration and moment of earthquakes in the Indian Peninsula using love waveforms

Love waves recorded by a long-period seismograph at New Delhi (NDI) from seven earthquakes of magnitude 4.3 to 5.2 in Koyna and Bhatsa on the western coast and one earthquake in Ongole on the eastern coast of the Indian Peninsula have been used to determine the seismic moment for each of the earthquakes by waveform modeling. Transverse component of the synthetic seismogram shows that the maximum amplitude of waveform decreases with an increase of source duration. Thus for an evaluation of the seismic moment by equating the amplitude level of the observed and synthetic waveforms, we must know the source duration. The synthetic seismogram also indicates that a short source duration gives rise to a small but sharp pulse and this pulse is interpreted as anLg wave. Comparison of the observed and synthetic waveforms has been used for a simultaneous evaluation of the source duration and seismic moment. The source durations are found to vary between 2.2 and 4.4 s; for earthquakes with a magnitude range between 4.3 and 5.2 these durations are slightly higher than normal. We obtain moment (M ₀) of Ongole earthquake (M _L =5.1)as 1.7×10²⁴ dyne-cm; moments of Koyna and Bhatsa earthquakes (4.3M _L 5.2) on the western coast lie between 0.7×10²³ and 3.6×10²³ dyne-cm. Moment (M ₀)-magnitude (M _L ) relation logM ₀=1.5M _L +16.0 for the western United States region agrees as well, in general, with the results for the earthquakes in the Indian Peninsula.     

Temporal variation of body wave attenuation as related to two earthquake doublets in W. Greece

In this research four earthquakes, which are considered to compose two earthquake doublets, recorded prior to and after a magnitudeM _s =5.0 and a magnitudeM _s =4.8 event in W. Greece are used to derive temporal variations ofP-wave attenuation in the region.Spectral ratios at four stations are computed and the results indicated a variation (increase) ofQ of the order of 15–20%. To confirm that this variation is not an artifact due to changes of the source parameters, a smaller event which occurred at the same hypocentre was used as a Green function and the deconvolution proved that the earthquakes of one of the doublet possessed the same source parameters.The outcome of this research verifies the possible role of the migration of fluids in the crust in the focal region and their effect on the attenuation of seismic waves.     

Source parameters of the earthquakes of the Baikal rift system

The dynamic parameters of the earthquake source—the seismic moment, the moment magnitude, the source radius, the stress drop, and the amplitude of displacement—are determined by the amplitude Fourier spectra of the body shear waves (S-waves) for 62 earthquakes of the Baikal rift system with the energy class of K _P = 9.1–15.7. In the calculations I used the classical Brune model. The seismic moment of the earthquakes being investigated changes from 3.65 × 10¹¹ N m to 1.35 × 10¹⁸ N m, and the radii of earthquake sources vary from 390 m to 1.84 km. The values of the drop in stress Δσ grow with an increase in the seismic moment up to 1.7 × 10⁸ Pa. For the group of weak earthquakes (M _w = 1.7–3.3), extremely low values of the drop in stress 10³–10⁴ Pa are observed. The maximum amplitude of displacement in the source amounts to 5.95 m. The empirical equations between the seismic moment and the other dynamic parameters of the source are determined. The regional dependence of the seismic moment and energy class is obtained: log M ₀ ± 0.60 = 1.03K _P + 3.17. The character of the relationship between the seismic moment and the corner frequency indicates that the classical scaling law of the seismic spectrum for the earthquakes in question is not fulfilled. The obtained estimates of the dynamic parameters are in satisfactory agreement with the published data concerning the analogous parameters of the other rift zones, which reflects the general regular patterns of the destruction of the lithosphere and the seismicity in the extension zones of the lithosphere.     

Quantification of major earthquake tsunamis of the Japan Sea

The size of major tsunamigenic earthquakes which occurred in the Japan Sea is quantified on the basis of seismic and tsunamigenic source parameters. The tsunami magnitude M_t is determined from the instrumental tsunami-wave amplitudes. The M_t values thus obtained are on average 0.2 units larger than the values of moment magnitude M_w, though the M_t scale has originally been adjusted to agree with M_w. Moreover, the volume of displaced water at the source is on average 2.3 times as large as that for the Pacific events with a comparable M_w. Nevertheless, the observed height of the sea-level disturbance at the source is found consistent with the amount of crustal deformation computed for the seismic fault models. These results indicate that the tsunami source potential itself is large for M_w in comparison with the Pacific events. The large source potential is explained in terms of the effective difference both in the rigidity of the source medium and in the geometry of the fault motion. For the Japan Sea events, the M_t scale still provides the physical measure of the tsunami potential, and M_t minus 0.2 corresponds to M_w. This predicts that the maximum amplitude of tsunami waves from Japan Sea earthquakes is at least two times as large as that from Pacific earthquakes with a comparable M_w.     

陕西地区小微震震源机制研究

小微震事件的震源机制是区域应力场及诸多地球动力学研究的基础资料。陕西地区为多个地震带的交汇区,近些年积累了丰富的小微震波形资料。运用新近发展的适用于求解小微震震源机制的广义极性振幅技术(GPAT),结合陕西2015地壳速度模型,求解陕西测震台网2011年4月至2015年12月间记录的121次ML1.5~3.5事件的震源机制。反演结果表明:(1)以上事件的震源机制大部分为走滑及正断类型,其比例占64.5%;逆断型机制占22.3%。(2)反演震源机制得到的震源深度与定位深度具有良好的一致性;矩震级与近震震级间存在差别,且这种差别随事件的变小而增大。(3)对比渭河断陷带相关研究成果,验证了该区域震源机制以正断型为主,具有拉张应力状态。     

Comparison between different earthquake magnitudes determined by China Seismograph Network

By linear regression and orthogonal regression methods, comparisons are made between different magnitudes (lo-cal magnitude ML, surface wave magnitudes MS and MS7, long-period body wave magnitude mB and short-period body wave magnitude mb) determined by Institute of Geophysics, China Earthquake Administration, on the basis of observation data collected by China Seismograph Network between 1983 and 2004. Empirical relations between different magnitudes have been obtained. The result shows that: 1 As different magnitude scales reflect radiated energy by seismic waves within different periods, earthquake magnitudes can be described more objectively by using different scales for earthquakes of different magnitudes. When the epicentral distance is less than 1 000 km, local magnitude ML can be a preferable scale; In case M<4.5, there is little difference between the magnitude scales; In case 4.5MS, i.e., MS underestimates magnitudes of such events, therefore, mB can be a better choice; In case M>6.0, MS>mB>mb, both mB and mb underestimate the magnitudes, so MS is a preferable scale for deter-mining magnitudes of such events (6.08.5, a saturation phenomenon appears in MS, which cannot give an accurate reflection of the magnitudes of such large events; 2 In China, when the epicentral distance is less than 1 000 km, there is almost no difference between ML and MS, and thus there is no need to convert be-tween the two magnitudes in practice; 3 Although MS and MS7 are both surface wave magnitudes, MS is in general greater than MS7 by 0.2~0.3 magnitude, because different instruments and calculation formulae are used; 4 mB is almost equal to mb for earthquakes around mB4.0, but mB is larger than mb for those of mB≥4.5, because the periods of seismic waves used for measuring mB and mb are different though the calculation formulae are the same.     

Moment Magnitude and Its Calculation

In this paper, we give a brief introduction to the proposal and development history of the earthquake magnitude concept. Moment magnitude M_W is the best physical quantity for measuring earthquakes. Compared with other magnitude scales used traditionally, moment magnitude is not saturated for all earthquakes, regardless of big and small earthquakes, deep and shallow earthquakes, far field and near field seismic data, geodetic and geological data, moment magnitude can be measured, and can be connected with well-known magnitude scales such as surface wave magnitude M_S. Moment magnitude is a uniform magnitude scale, which is suitable for statistics with wide magnitude range. Moment magnitude is the preferred magnitude selected by the International Seismological community, and it is preferred by the departments responsible for publishing seismic information to the public.Moment magnitude is a uniform magnitude scale, which is suitable for statistics with wide magnitude range. Moment magnitude is a preferred magnitude for international seismology, it is preferred by the agency responsible for providing information about earthquakes to the public. We provide all formulas used in the calculation of moment magnitude, and the calculation steps in detail. We also analyzed some problems and rules to solve these problems by using different formulas and numerical value calculation steps.     

Empirical Global Relations Converting M S and m b to Moment Magnitude

The existence of several magnitude scales used by seismological centers all over the world and the compilation of earthquake catalogs by many authors have rendered globally valid relations connecting magnitude scales a necessity. This would allow the creation of a homogeneous global earthquake catalog, a useful tool for earthquake research. Of special interest is the definition of global relations converting different magnitude scales to the most reliable and useful scale of magnitude, the moment magnitude, M _W. In order to accomplish this, a very large sample of data from international seismological sources (ISC, NEIC, HRVD, etc.) has been collected and processed. The magnitude scales tested against M _W are the surface wave magnitude, M _S, the body wave magnitude, m _b, and the local magnitude, M _L. The moment magnitudes adopted have been taken from the CMT solutions of HRVD and USGS. The data set used in this study contains 20,407 earthquakes, which occurred all over the world during the time period 1.1.1976–31.5.2003, for which moment magnitudes are available. It is shown that well-defined relations hold between M _W and m _b and M _S and that these relations can be reliably used for compiling homogeneous, with respect to magnitude, earthquake catalogs.     

Source modeling of the Hsingtai,China earthquakes of March 1966

The Hsingtai, China earthquakes of March 1966 were a series of destructive earthquakes associated with the Shu-lu graben. Five strong shocks of M_s ≥ 6 occurred within a period of less than a month, the largest of which was M_s 7.2. Body and surface waves over the period range from several to 100 s have been modeled for the four largest events using synthetic seismograms in the time domain and spectral analysis in the frequency domain. Data from ground deformation, local geology, regional seismic network, and teleseismic joint epicenter determination have also been used to constrain the source model and the rupture process.The fault mechanism of the Hsingtai sequence was mainly strike-slip with a small component of normal dip-slip. The strikes of the four largest shocks range from ～ N26° to 30°E, approximately along strike of the major faults of the Shu-lu graben and the aftershock distribution. The source mechanisms can be explained with a NNW-SSE extensional stress and a NEE-SWW compressional stress acting in the area. The major shocks all had focal depths ～ 10 km.The four largest shocks in the sequence were characterized by a relatively simple and smooth dislocation time history. The durations of the far-field source time functions ranged from 3.5 to 5 s, while the rise times were all ～ 1 s. The seismic moments of the four largest earthquakes ranged from 1.43 × 10²⁵ to 1.51 × 10²⁶ dyne cm^?1. The fault sizes of the four events were very close. Assuming circular faults, the diameters of the four events were determined to be between 10 and 14 km. Stress drops varied from ～ 52 to 194 bars. A trend of increasing stress drop with earthquake size was observed.A survey of stress drop determinations for 15 major intraplate earthquakes shows that on the average the magnitude of stress drop of oceanic intraplate earthquakes and passive continental margin events is higher (～ 200 to several hundred bars) than that of continental intraplate earthquakes (～ 100 bars or less).     

Calibration of magnitude scales for earthquakes of the Mediterranean

In order to provide the tools for uniform size determination for Mediterranean earthquakes over the last 50-year period of instrumental seismology, we have regressed the magnitude determinations for 220 earthquakes of the European-Mediterranean region over the 1977–1991 period, reported by three international centres, 11 national and regional networks and 101 individual stations and observatories, using seismic moments from the Harvard CMTs. We calibrate M(M₀) regression curves for the magnitude scales commonly used for Mediterranean earthquakes (M_L, M_WA, m_b, M_S, M_LH, M_LV, M_D, M); we also calibrate static corrections or specific regressions for individual observatories and we verify the reliability of the reports of different organizations and observatories. Our analysis shows that the teleseismic magnitudes (m_b, M_S) computed by international centers (ISC, NEIC) provide good measures of earthquake size, with low standard deviations (0.17–0.23), allowing one to regress stable regional calibrations with respect to the seismic moment and to correct systematic biases such as the hypocentral depth for M_S and the radiation pattern for m_b; while m_b is commonly reputed to be an inadequate measure of earthquake size, we find that the ISC m_b is still today the most precise measure to use to regress M_W and M₀ for earthquakes of the European-Mediterranean region; few individual observatories report teleseismic magnitudes requiring specific dynamic calibrations (BJI, MOS). Regional surface-wave magnitudes (M_LV, M_LH) reported in Eastern Europe generally provide reliable measures of earthquake size, with standard deviations often in the 0.25–0.35 range; the introduction of a small (±0.1–0.2) static station correction is sometimes required. While the Richter magnitude M_L is the measure of earthquake size most commonly reported in the press whenever an earthquake strikes, we find that M_L has not been computed in the European-Mediterranean in the last 15 years; the reported local magnitudes M_WA and M_L do not conform to the Richter formula and are of poor quality and little use, with few exceptions requiring ad hoc calibrations similar to the M_S regression (EMSC, ATH). The duration magnitude M_D used by most seismic networks confirms that its use requires accurate station calibrations and should be restricted only to events with low seismic moments.